In: Chemistry
The lab technician Anna Lytic adds 2.20 mol KOH to 1.00 L of 0.5 M Al(NO3)3. What is the concentration of aluminum ions after the aluminum nitrate has reacted with the potassium hydroxide? Kf = 3.0 ´ 1033 for Al(OH)4– Answer: 1*10^(-31). Please explain the process thoroughly.
The chemical reactions taking place are -
KOH + Al(NO3)3 -> KNO3 + Al(OH)3
and then Al(OH)3 + KOH -> Al(OH)4- + K+ ------- Eqn #2
If we balance the OH atoms of the first equation by multiplying KOH by 3 and KNO3 by 3 we get
3KOH + Al(NO3)3 -> 3KNO3 + Al(OH)3
Adding this equation with Eqn #2 we get
3KOH + Al(NO3)3 + Al(OH)3 + KOH -> 3KNO3 + Al(OH)3 + Al(OH)4- + K+
Cancelling out common terms of Al(OH)3 we get
4KOH + Al(NO3)3 -> 3KNO3+ Al(OH)4- + K+ --------- Final equation
Init 2.2 0.5 0 0 0
Comp 0.2 0 1.5 0.5 0.5
So, here we can see for every 1 mole of Al(NO3)3 we need 4 moles of KOH
KOH , Al(NO3)3 and KNO3 will dissociate in ions in the aqeuous medium to from K+ , OH- , Al+3, NO3- ions
So, Final equation can be written as -
4K+ +4OH- + Al+3 + 3NO3- -> 3K+ + 3NO3- + Al(OH)4- + K+
Cancelling out common ions we get -
4OH- + Al+3 -> Al(OH)4- ----- final ionic equation
Initially, we have 1L 0.5M solution of Al(NO3)3 which will contain 0.5*1 = 0.5 moles of Al(NO3)3
as molarity = moles/Vol in L so, moles = molairty*vol.
So, for 0.5 moles of Al(NO3)3 we will need 0.5*4 moles = 2 moles of KOH (from the final equation)
As Kf value is so high the reaction will be almost complete so, at the end of the reaction we will have 2.2 - 2 = 0.2 moles of KOH and 0.5 moles of Al(OH)4- (from the final equation)
Kf is the constant of formation of Al(OH)4- which can be calculated as from the final ionic reaction as
Kf = [Al(OH)4-]/[OH-]4[Al+3] where [Al(OH)4-] , [OH-], [Al+3] are the final concentrations.
After completion concentration of OH- = KOH = 0.2 M and [Al(OH)4-] = 0.5 M (here molarity = moles as volume is 1L and molarity = no.of moles / vol in L)
So, 3*103 = 0.5/(0.24)*[Al+3] so, [Al+3] = (0.5/0.24) * 10-33 = 1.04 * 10-31 which is roughly 1*10-31 M